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An undecidable property of definite integrals
Author(s):
Daniel
T.
Stallworth;
Fred
W.
Roush
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2147-2148.
MSC (1991):
Primary 03B25
MathSciNet review:
1377008
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Abstract:
We show that it is undecidable whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic.
References:
- [A]
- A. Adler, Some recursively unsolvable problems in analysis, Proc. Amer. Math. Soc. 22 (1969), 523-526. MR 40:1277
- [DL]
- J. Denef and L. Lipschitz, Decision problems for differential equations, J. Symbolic Logic 54 (1989), 941-949. MR 91b:03074
- [R]
- D. Richardson, Some undecidable problems involving elementary functions of a real variable, J. Symbolic Logic 33 (1968), 514-520. MR 39:1330
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Additional Information:
Daniel
T.
Stallworth
Affiliation:
Department of Mathematics, Alabama State University, Montgomery, Alabama 36101-0271
Fred
W.
Roush
Affiliation:
Department of Mathematics, Alabama State University, Montgomery, Alabama 36101-0271
Email:
froush@asu.alasu.edu
DOI:
10.1090/S0002-9939-97-03822-7
PII:
S 0002-9939(97)03822-7
Keywords:
Undecidability of definite integrals
Received by editor(s):
February 18, 1994
Received by editor(s) in revised form:
January 29, 1996
Communicated by:
Andreas R. Blass
Copyright of article:
Copyright
1997,
American Mathematical Society
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